Consider the linear system of equations below 3x1 − x2 + x3 = 1 3x1 +...

Consider the linear system of equations below
3x1 − x2 + x3 = 1
3x1 + 6x2 + 2x3 = 0
3x1 + 3x2 + 7x3 = 4
i. Use the Gauss-Jacobi iterative technique with x
(0) = 0 to find
approximate solution to the system above up to the third step
ii. Use the Gauss-Seidel iterative technique with x
(0) = 0 to find
approximate solution to the third step

Expert Solution

Colby Messinger answered 2 years ago

Consider the linear system of equations 2x1 − 6x2 − x3 = −38 −3x1 − x2...

Consider the linear system of equations 2x1 − 6x2 − x3 = −38 −3x1 − x2 + 7x3 = −34 −8x1 + x2 − 2x3 = −20 With an initial guess x (0) = [0, 0, 0]T solve the system using Gauss-Seidel method.

1. Solve the following system: 2x1- 6x2- x3 = -38 -3x1–x2 +7x3 = -34 -8x1 +x2...

1. Solve the following system: 2x1- 6x2- x3 = -38 -3x1–x2 +7x3 = -34 -8x1 +x2 – 2x3 = -20 By: a. LU Factorization b. Gauss-Siedel Method, error less that10-4 Hint (pivoting is needed, switch rows).

Consider the following linear optimization model. Z = 3x1+ 6x2+ 2x3 st 3x1 +4x2 + x3...

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(a) Consider three positive integers, x1, x2, x3, which satisfy the inequality below: x1 +x2 +x3...

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Is the following map linear? a) F(x1,x2,x3)=(0,0) b) L:R2→R2 defined by L(x1,x2)=(3x1−2x2,x2) c) f:R→R defined by...

Is the following map linear? a) F(x1,x2,x3)=(0,0) b) L:R2→R2 defined by L(x1,x2)=(3x1−2x2,x2) c) f:R→R defined by f(x)=2x

Solve the following set of equations with LU factorization with pivoting: 3x1 -2x2 + x3 =...

Solve the following set of equations with LU factorization with pivoting: 3x1 -2x2 + x3 = -10 2x1 + 6x2- 4x3 = 44 -8x1 -2x2 + 5x3 = -26 Please show all steps

Given the following LP max z = 2x1 + x2 + x3 s. t. 3x1 -...

Given the following LP max z = 2x1 + x2 + x3 s. t. 3x1 - x2 <= 8 x2 +x3 <= 4 x1,x3 >= 0, x2 urs (unrestricted in sign) A. Reformulate this LP such that 1)All decision variables are non-negative. 2) All functional constraints are equality constraints B. Set up the initial simplex tableau. C. Determine which variable should enter the basis and which variable should leave.

Consider a general system of linear equations with m equations in n variables, called system I....

Consider a general system of linear equations with m equations in n variables, called system I. Let system II be the system obtained from system I by multiplying equation i by a nonzero real number c. Prove that system I and system II are equivalent.

Consider a homogeneous system of linear equations with m equations and n variables. (i) Prove that...

Consider a homogeneous system of linear equations with m equations and n variables. (i) Prove that this system is consistent. (ii) Prove that if m < n then the system has infinitely many solutions. Hint: Use r (the number of pivot columns) of the augmented matrix.

Consider the systems of equations −3x1 +9x2 +4x3 −5x4 −4x5 = 5 −3x1 +9x2 +3x3 −6x4...

Consider the systems of equations −3x1 +9x2 +4x3 −5x4 −4x5 = 5 −3x1 +9x2 +3x3 −6x4 −3x5 = 3 x1 −3x2 −x3 +2x4 +x5 = −1 (a) Write this as a matrix equation Ax = b. (b) Find the general solution. (c) What is Rank(A)? (d) Does Ax = c have a solution for every c in R3? Explain.

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